According to the OHIO BMV web site, it says:

Effective August 29, 2007, customers will no longer be required to show proof of Social Security Number on initial vehicle registrations if an Ohio driver license or Ohio identification card is presented. Customers who do not present an Ohio driver license or Ohio identification card on an initial registration will be required to prove their Social Security Number by presenting a document from the acceptable document list.

(retrieved 12/3/2010, http://www.bmv.ohio.gov/index.stm)

Therefore, new international student with a valid F1 visa and I-20 status can have an Ohio Drivers' license first, and then use this ID to register her/his vehicle without SSN.  If BMV still requires a SSN, s/he can ask the agent to provide s/he with letter stating that the BMV requires a SSN, and take it to the SS administration to get one.

S/he might want to try the 30 day temp tag using foreign drivers license.